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An Abstract Model of a Cortical Hypercolumn AN ABSTRACT MODEL OF A CORTICAL HYPERCOLUMN Baran Çürüklü1, Anders Lansner2 1Department of Computer Engineering, Mälardalen University, S-72123 Västerås, Sweden 2Department of Numerical Analysis and Computing Science, Royal Institute of Technology, S-100 44 Stockholm, Sweden ABSTRACT preferred stimulus was reported to be lower than to preferred stimulus. An abstract model of a cortical hypercolumn is presented. According to the findings by Hubel and Wiesel [16] This model could replicate experimental findings relating the primary visual cortex has a modular structure. It is to the orientation tuning mechanism in the primary visual composed of orientation minicolumns each one cortex. Properties of the orientation selective cells in the comprising some hundreds of pyramidal cells and a primary visual cortex like, contrast-invariance and smaller number of inhibitory interneurons of different response saturation were demonstrated in simulations. We kinds. Contrast edge orientation is coded such that the hypothesize that broadly tuned inhibition and local cells in each orientation minicolumn respond selectively excitatory connections are sufficient for achieving this to a quite broad interval of orientations. Further, the behavior. We have shown that the local intracortical orientation hypercolumn contains orientation minicolumns connectivity of the model is to some extent biologically with response properties distributed over all angles, and plausible. thus represents the local edge orientation pertinent to a given point in visual space. A similar modular arrangement is found in many other cortical areas, e.g. rodent whisker barrels [15]. 1. INTRODUCTION The Bayesian Confidence Propagation Neural Network model (BCPNN) has been developed in analogy Most neurons in the primary visual cortex (V1) with this possibly generic cortical structure [14]. This is respond to specific orientations even though relay cells in an abstract neural network model in which each unit the lateral geniculate nucleus (LGN), that carries the corresponds to a cortical minicolumn. The network is information from retina to V1, does not show evidence of partitioned into hypercolumn-like modules and the orientation selectivity. It is not known in detail how summed activity within each hypercolumn is normalized orientation selectivity of the cells in V1 emerges and the to one. issue is hotly debated (for a recent review see Ferster et The above network model relates to the so-called al., [9]). Hubel and Wiesel [10] proposed that orientation normalization models of V1 proposed by Albrecht et al. selectivity of simple cells in V1 was a consequence of [20] and Heeger [21] that address properties of simple synaptic input from LGN. Still today the Hubel and cells mentioned above. These assume that input from the Wiesel feedforward model serves as a model of thalamic LGN grows linearly with contrast stimulus. This input is input to cortex. However many of the properties of divided by a linearly growing inhibitory input. The effect orientation selective cells in V1 cannot be predicted by is division of the input from the LGN and that the such a feedforward model. Contrast-invariance of summed activity of the cells in a hypercolumn is orientation tuning seen by simple and complex cells is normalized. This would correspond to saturation of a cells perhaps the most striking example. As contrast increases activity. Later Carandini et al. [22,23] proposed that a the height of the response curve increases while the width pool of cells with different preferred orientations and remains almost constant [11,12,13]. spatial frequencies drives the shunting inhibition. It was also shown that response to contrast stimulus Cross-orientation inhibition is yet another feature of increases over approximately 50-60% of the response cortical simple and complex cells. Response to range and this behavior is followed by a rapid saturation superposition of two gratings is less than sum of each and normalization of the cells activity [13]. The saturation response alone [8,25]. Morrone et al. [8] suggested that level seems to be determined by stimulus property this inhibition arises from a pool of cells with different (orientation, spatial frequency) and not by electrical orientations. The cross-inhibition effect could be properties of the cells. Maximum response to non- A B 180° 90° 0° 900 µm C Output from the minicolumn D 2 chandelier 100 % Percent of cells maximum Output response layer Network of 12 excitatory cells One 600 µm basket Network cell of 11 excitatory Input cells layer 40 % 3 chandelier cells 56 µm Contrast 100 % Input from cortex and LGN Figure 1. A, The hypothesized repetitive layout of the cat V1 D, A scheme showing the activity of the excitatory cells demonstrated by 7 hypercolumns. B, The partial in two minicolumns with preferred orientation (bottom hypercolumn model used during the simulations consisted solid lines) and non-preferred orientation (bottom dashed of 17 minicolumns. C, A scheme showing one of the lines). Input layer excitatory cells (exponential curves) are subsampled orientation minicolumns and the basket cell driving the basket cell (thick top curve). The output layer representing the pool of inhibitory cells. Excitatory cells excitatory cells (sigmoidal curves) are normalized when in the input layer are connected to the basket cell, and the the basket cell’s activity increases linearly. basket cell inhibits the excitatory cells in the output layer. explained by a shunting inhibition proposed by the two excitatory neurons inside a minicolumn layer was a normalization models [22,23]. function of the distance between them [6]. Here we present an abstract model of a cortical The implication of this scheme for the output layer is hypercolumn derived from the above-mentioned BCPNN that, the distribution (in terms of orientation) of the architecture. Our main intention has been to address inhibitory input to an excitatory cell is broader than the response saturation and contrast-invariance of orientation excitatory input. This is because the basket cell represents tuning behaviors of cortical cells. Initial tests were a pool of orientation specific neurons inhibiting a pool of showing that cross-orientation inhibition was also excitatory neurons with all possible preferred orientation. prominent. All these behaviors could be achieved by a Even though the connectivity pattern seen in the output very simple network architecture (Fig. 1). layer is very simple, it is still biologically plausible. Kisvárday et al. [27] reported that, in an area of the size of 2. NETWORK MODEL cat V1 hypercolumn, 56 % of the excitatory and 47 % of the inhibitory connections were at iso-orientation, while The foundation of our network model is the columnar cross-inhibition was shown by 14 % of excitatory and 20 organization seen in V1 and elsewhere in the cortex [16]. % of inhibitory connections respectively. This indicates We assume that V1 is composed of repetitive structures, that, the inhibitory network is less orientation specific so-called minicolumns, and that these minicolumns rotate than the excitatory network. A study based on ferret around hypothetical centers [18], and form hypercolumns prefrontal microcircuits is also pointing in the direction of (Fig. 1a). In our model a hypercolumn is represented by a the basket cells as responsible for gain control of the local finite number of minicolumns, each representing a cortical network [26]. particular orientation (Fig. 1b). For sake of simplicity we Besides the basket cell, there were other inhibitory decided to use a partial hypercolumn model composed of cells in the model. These cells were the local inhibitory 17 subsampled orientation minicolumns, ranging from 0° chandelier cells [28] located inside the minicolumns, and to 180°, with the angular distance of 11.25° between two hence inhibiting excitatory cells with the same orientation successive ones (Fig. 1b). The diameter of the cylinder preference. In the input layer three chandelier cells shaped minicolumns was 56 µm, as a consequence of the inhibited an excitatory cell, while two chandelier cells study done by Peters et al. [17] on cat V1. In that study, it inhibited the excitatory cells in the output layer. was reported that apical dendrites of layer V pyramid cells Cortical neurons are known for their irregular spiking formed clusters with a center-to-center spacing of about activity [3,4], and were thus modeled as Poisson 56 µm, which provides an estimate of the mean distance processes. As the kernel of the Poisson process we used a between two successive minicolumns. The circular leaky integrate-and-fire model [1,2]. The role of the leaky arrangement of the minicolumns gives the biologically integrate-and-fire model was to sum the presynaptic plausible hypercolumn diameter of 900 µm for cat V1. inputs to generate the membrane potential of the cells. The minicolumns has a height of 600 µm, and are Maximum frequency of the excitatory and the inhibitory abstractions of the layer II-IV of cat V1 [17]. Each of the neurons were 100 Hz and 300 Hz respectively. Half- subsampled minicolumns is composed of 28 neurons (Fig. height of the IPSPs were 10 ms, and 15 ms for the EPSPs. 1c) and the neuron population is heterogeneous with all Mean amplitudes of the EPSPs inside the minicolumns values sampled from a uniform distribution with a were 0.94 mV for the input layer, and 9.4 mV for the standard deviation of 10%. output layer. The strength of the synaptic connection The hypercolumn model consists of two separate between the input layer excitatory cells and the basket cell layers with two different tasks in order to achieve was set to give an EPSP of 3.5 mV. IPSPs generated by normalization behavior proposed by the BCPNN model the chandelier cells had a mean of -3.2 mV, and that of the (Fig. 1c). It will be shown later that the excitatory neuron basket cell was -55.1 mV. Observe that the values are in the output layer replicates experimental findings exaggerated, specially the IPSP generated by the basket relating to the orientation tuning mechanism in V1.
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